Question
Two pipes A and B can fill a tank in 12 hours and 15
hours, respectively. Another pipe C can empty the tank in 10 hours. If all three pipes are opened together, how long will it take to fill the tank if C is closed after 5 hours?Solution
Work done by A, B, and C together in 1 hour = 1/12 + 1/15 - 1/10 = (5 + 4 - 6)/60 = 3/60 = 1/20. In 5 hours, they fill = 5 × 1/20 = 1/4 of the tank. Remaining tank = 1 - 1/4 = 3/4. After C is closed, work done by A and B in 1 hour = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20. Time to fill 3/4 of the tank = (3/4) ÷ (3/20) = 5 hours. Total time = 5 + 5 = 10 hours. Correct option: c
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